Interpolation of room impulse responses in 3d using compressed sensing
Interpolation of room impulse responses in 3d using compressed sensing
复制标题
使用压缩感知对 3d 空间脉冲响应进行插值
DOI：
10.1002/j.1538-7305.1967.tb04231.x
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发表时间：
2012
影响因子：
--
通讯作者：
F. Ollivier
中科院分区：
文献类型：
--
作者：
R. Mignot;L. Daudet;F. Ollivier
在房间中，声源和接收器之间的声传递由所谓的房间脉冲响应描述，其取决于位置和房间特性。根据采样定理，直接测量3D空间域内的声学脉冲响应的全部集合将需要不合理的大量测量。然而，考虑到声波场在一些字典中是稀疏的，压缩感知框架允许利用减少的测量（麦克风）集合来恢复全波场，但是提出了具有挑战性的计算和存储器问题。在本文中，我们展示了两个稀疏性假设的波场，我们推导出两个实用的算法的波场估计。第一种方法利用模态理论对低频房间脉冲响应进行采样（频率稀疏），第二种方法利用图像源方法对早期反射进行插值（时间稀疏）。这两种互补的方法进行了验证，使用120麦克风3D阵列的数值和实验测量，并给出作为麦克风的数量的函数的结果。
In a room, the acoustic transfer between a source and a receiver is described by the so-called Room Impulse Response, which depends on both positions and the room characteristics. According to the sampling theorem, directly measuring the full set of acoustic impulse responses within a 3D-space domain would require an unreasonably large number of measurements. Nevertheless, considering that the acoustic wavefield is sparse in some dictionaries, the Compressed Sensing framework allows the recovery of the full wavefield with a reduced set of measurements (microphones), but raises challenging computational and memory issues. In this paper, we exhibit two sparsity assumptions of the wavefield and we derive two practical algorithms for the wavefield estimation. The first one takes advantage of the Modal Theory for the sampling of the Room Impulse Responses in low frequencies (sparsity in frequency), and the second one exploits the Image Source Method for the interpolation of the early reflections (sparsity in time). These two complementary approaches are validated both by numerical and experimental measurements using a 120-microphone 3D array, and results are given as a function of the number of microphones.